The sum of two positive integers is always positive but a (positive integer) – (positive integer) can be positive or negative. What about a. (positive) – (negative) b. (positive) + (negative) c. (negative) + (negative) d. (negative) – (negative) e. (negative) – (positive) f. (negative) + (positive)
Always positive
Can be positive, negative, or zero
Always negative
Can be positive, negative, or zero
Always negative
Can be positive, negative, or zero
Explanation
(a) Subtracting a negative is the same as adding the corresponding positive. Positive + Positive = Positive. (b) Depends on which number has larger magnitude. If positive is larger, result is positive. If negative is larger, result is negative. If equal, result is zero. (c) Adding two negative numbers always gives a negative result with magnitudes added. (d) Depends on which negative has larger magnitude. −3 − (−5) = +2, −5 − (−3) = −2, −3 − (−3) = 0. (e) Subtracting a positive from a negative always gives a more negative result. (f) Same as (b). Depends on which number has larger magnitude.